Spring (March–May) and autumn (September–November) are best — daytime highs of 18–27°C, cool nights, very little rain. Summer is hot (32–37°C is normal and 40°C is possible) and winter mornings can be sharply cold despite the desert sun.
The big event is the Roswell UFO Festival, held every year over the Independence Day weekend (early July). Tens of thousands of visitors arrive for the parade, costume contests, alien-themed art shows, lectures by UFOlogists, and a generally festive embrace of the town's reputation. Book accommodation months in advance and accept that it will be hot — but it's the obvious time to visit if the UFO angle is what brings you.
October to February is sandhill crane season at Bitter Lake — a serious draw for birders.